Slant ruled surfaces and slant developable surfaces of spacelike curves in Lorentz-Minkowski 3-space. (English) Zbl 1499.53050
Summary: In this paper, by means of the Lorentzian Frenet frame along a spacelike curve in Lorentz-Minkowski 3-space, we construct slant ruled surfaces and slant developable surfaces with different director curves which belong to one-parameter families of the pseudo-spheres in this space. Moreover, for each slant ruled surface with each director curve, we search if this slant ruled surface has any singularities or not. Furthermore, for the cases in which the singularities appear, we determine the singularities of non-lightlike and non-cylindrical slant developable surfaces and also investigate the singularities of slant ruled surfaces.
MSC:
| 53A35 | Non-Euclidean differential geometry |
| 53B30 | Local differential geometry of Lorentz metrics, indefinite metrics |
| 57R45 | Singularities of differentiable mappings in differential topology |
| 58K05 | Critical points of functions and mappings on manifolds |
| 53A25 | Differential line geometry |
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